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Stochastic Analysis Of Flow And Transport In Porous Media
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Book Synopsis Stochastic Analysis of Flow and Transport in Porous Media by : Veronika S. Vasylkivska
Download or read book Stochastic Analysis of Flow and Transport in Porous Media written by Veronika S. Vasylkivska and published by . This book was released on 2012 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties such as permeability, porosity and diffusivity. In many situations description of properties of the porous media is aided by a limited number of observations at fixed points. These observations constrain the randomness of the field and lead to conditional simulations. In this work we propose a method of simulating the random fields which respect the observed data. An advantage of our method is that in the case that additional data becomes available it can be easily incorporated into subsequent representations. The proposed method is based on infinite series representations of random fields. We provide truncation error estimates which bound the discrepancy between the truncated series and the random field. We additionally provide the expansions for some processes that have not yet appeared in the literature. There are several approaches to efficient numerical computations for partial differential equations with random parameters. In this work we compare the solutions of flow and transport equations obtained by conditional simulations with Monte Carlo (MC) and stochastic collocation (SC) methods. Due to its simplicity MC method is one of the most popular methods used for the solution of stochastic equations. However, it is computationally expensive. The SC method is functionally similar to the MC method but it provides the faster convergence of the statistical moments of the solutions through the use of the carefully chosen collocation points at which the flow and transport equations are solved. We show that for both methods the conditioning on measurements helps to reduce the uncertainty of the solutions of the flow and transport equations. This especially holds in the neighborhood of the conditioning points. Conditioning reduces the variances of solutions helping to quantify the uncertainty in the output of the flow and transport equations.
Book Synopsis An Analysis of the Stochastic Approaches to the Problems of Flow and Transport in Porous Media by : David W. Dean
Download or read book An Analysis of the Stochastic Approaches to the Problems of Flow and Transport in Porous Media written by David W. Dean and published by . This book was released on 1996 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Analysis Of Flow And Solute Transport In Heterogeneous Porous Media Using Perturbation Approach by :
Download or read book Stochastic Analysis Of Flow And Solute Transport In Heterogeneous Porous Media Using Perturbation Approach written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of flow and solute transport problem in porous media are affected by uncertainty inbuilt both in boundary conditions and spatial variability in system parameters. The experimental investigation reveals that the parameters may vary in various scales by several orders. These affect the solute plume characteristics in field-scale problem and cause uncertainty in the prediction of concentration. The main focus of the present thesis is to analyze the probabilistic behavior of solute concentration in three dimensional(3-D) heterogeneous porous media. The framework for the probabilistic analysis has been developed using perturbation approach for both spectral based analytical and finite element based numerical method. The results of the probabilistic analysis are presented either in terms of solute plume characteristics or prediction uncertainty of the concentration. After providing a brief introduction on the role of stochastic analysis in subsurface hydrology in chapter 1, a detailed review of the literature is presented to establish the existing state-of-art in the research on the probabilistic analysis of flow and transport in simple and complex heterogeneous porous media in chapter 2. The literature review is mainly focused on the methods of solution of the stochastic differential equation. Perturbation based spectral method is often used for probabilistic analysis of flow and solute transport problem. Using this analytical method a nonlocal equation is solved to derive the expression of the spatial plume moments. The spatial plume moments represent the solute movement, spreading in an average sense. In chapter 3 of the present thesis, local dispersivity if also assumed to be random space function along with hydraulic conductivity. For various correlation coefficients of the random parameters, the results in terms of the field scale effective dispersivity are presented to demonstrate the effect of local dispersivity variation in space. The randomness of local.
Book Synopsis Stochastic Analysis of Flow and Transport in the Vadose Zone by : Alexander Yishan Sun
Download or read book Stochastic Analysis of Flow and Transport in the Vadose Zone written by Alexander Yishan Sun and published by . This book was released on 2000 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Methods for Flow in Porous Media by : Dongxiao Zhang
Download or read book Stochastic Methods for Flow in Porous Media written by Dongxiao Zhang and published by Elsevier. This book was released on 2001-10-11 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes Practical examples throughout the text Exercises at the end of each chapter reinforce specific concepts and techniques For the reader who is interested in hands-on experience, a number of computer codes are included and discussed
Book Synopsis An Analysis of the Stochastic Approaches to the Problems of Flow and Transport in Porous Media by : David W. Dean
Download or read book An Analysis of the Stochastic Approaches to the Problems of Flow and Transport in Porous Media written by David W. Dean and published by . This book was released on 1998 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Flow and Transport in Fractured Porous Media by : Peter Dietrich
Download or read book Flow and Transport in Fractured Porous Media written by Peter Dietrich and published by Springer Science & Business Media. This book was released on 2005-03-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the characterization of flow and transport in porous fractured media from experimental and modeling perspectives. The volume explores porous media problems, from the origin of the present natural porous structures, to their characterization, and various flow and transport phenomena that exist within the porous media. Examples are miscible displacements in porous media and fractured rock and the physical and chemical interactions within porous fractured aquifers. The book is a comprehensive presentation of investigations performed and analysed on different scales, supporting the understanding and application of experimental studies and numerical simulations.
Book Synopsis Subsurface Flow and Transport by : Gedeon Dagan
Download or read book Subsurface Flow and Transport written by Gedeon Dagan and published by Cambridge University Press. This book was released on 1997-09-04 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a major method in modelling the flow of water and transport of solutes in the subsurface, a subject of considerable interest in the exploitation and preservation of water resources. The stochastic approach allows the uncertainty which affects various properties and parameters to be incorporated in models of subsurface flow and transport. These much more realistic models are of greater use in, for example, modelling the transport and build-up of contaminants in groundwater. The volume is based on the second Kovacs Colloquium organised by the International Hydrological Programme (UNESCO) and the International Association of Hydrological Sciences. Fifteen leading scientists with international reputations review the latest developments in this area. The book is a valuable reference work for graduate students, research workers and professionals in government and public institutions, interested in hydrology, environmental issues, soil physics, petroleum engineering, geological engineering and applied mathematics.
Book Synopsis Fundamentals of Transport Phenomena in Porous Media by : Jacob Bear
Download or read book Fundamentals of Transport Phenomena in Porous Media written by Jacob Bear and published by Springer. This book was released on 1984-11-30 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Newark, Delaware, July 18-27, 1982
Book Synopsis Flow and Transport in Porous Media and Fractured Rock by : Muhammad Sahimi
Download or read book Flow and Transport in Porous Media and Fractured Rock written by Muhammad Sahimi and published by John Wiley & Sons. This book was released on 2011-05-09 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this standard reference of the field, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are considered. Two different approaches are discussed and contrasted with each other. The first approach is based on the classical equations of flow and transport, called 'continuum models'. The second approach is based on modern methods of statistical physics of disordered media; that is, on 'discrete models', which have become increasingly popular over the past 15 years. The book is unique in its scope, since (1) there is currently no book that compares the two approaches, and covers all important aspects of porous media problems; and (2) includes discussion of fractured rocks, which so far has been treated as a separate subject. Portions of the book would be suitable for an advanced undergraduate course. The book will be ideal for graduate courses on the subject, and can be used by chemical, petroleum, civil, environmental engineers, and geologists, as well as physicists, applied physicist and allied scientists that deal with various porous media problems.
Book Synopsis Stochastic Models of Flow and Transport in Multiple-scale Heterogeneous Porous Media by :
Download or read book Stochastic Models of Flow and Transport in Multiple-scale Heterogeneous Porous Media written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Modeling for Flow and Transport Through Porous Media by : Gedeon Dagan
Download or read book Mathematical Modeling for Flow and Transport Through Porous Media written by Gedeon Dagan and published by Springer Science & Business Media. This book was released on 1991 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of articles presented at an International Workshop on `Mathematical Modeling for Flow and Transport Through Porous Media'. The major topics of the meeting were free and moving boundary problems, structured media, multiphase flow, scale problems, stochastic aspects, parameter identification and optimization problems. The volume also represents a few contributions on the incorporation of chemical and biological processes in mathematical models for transport in porous media. The book is directed at researchers active in porous media, mathematical modeling, petroleum and geotechnical engineering and environmental sciences.
Book Synopsis Advances in Transport Phenomena in Porous Media by : Jacob Bear
Download or read book Advances in Transport Phenomena in Porous Media written by Jacob Bear and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lectures presented at the NATO ADVANCED STUDY INSTITUTE that took place at Newark, Delaware, U. S. A. , July 14-23, 1985. The objective of this meeting was to present and discuss selected topics associated with transport phenomena in porous media. By their very nature, porous media and phenomena of transport of extensive quantities that take place in them, are very complex. The solid matrix may be rigid, or deformable (elastically, or following some other constitutive relation), the void space may be occupied by one or more fluid phases. Each fluid phase may be composed of more than one component, with the various components capable of interacting among themselves and/or with the solid matrix. The transport process may be isothermal or non-isothermal, with or without phase changes. Porous medium domains in which extensive quantities, such as mass of a fluid phase, component of a fluid phase, or heat of the porous medium as a whole, are being transported occur in the practice in a variety of disciplines.
Book Synopsis Stochastic Models for Flow and Transport in Heterogeneous Porous Media by : Amir Hossein Delgoshaie
Download or read book Stochastic Models for Flow and Transport in Heterogeneous Porous Media written by Amir Hossein Delgoshaie and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling flow and transport in porous media is an important part of the decision-making process in managing crucial resources such as underground aquifers and hydrocarbon reservoirs, subsurface disposal of contaminants, and the design of battery systems. The multiscale nature of porous media, the heterogeneity of their properties and the uncertainty of our knowledge of these properties pose significant modeling challenges that have been the focus of extensive research. In this work, four important contributions are made to the modeling of flow and transport in porous systems. First, a non-local formulation is rigorously derived to find the average flow solution in multiscale porous media. Second, the stochastic representation of the flow problem is used for quantifying the flow uncertainty in cases with heterogeneous conductivity fields. An algorithm is proposed for using the Feynman-Kac formulation for one-dimensional elliptic problems with piecewise constant conductivity and various schemes were explored to improve the efficiency of particle tracking algorithms for both stochastic and deterministic flow problems. The third contribution of this work is the introduction of the stencil method, a discrete temporal Markov model for modeling transport in networks representing porous material. The stencil method simplifies the temporal models used to simulate mean transport in porous media. Finally, a fast discrete temporal Markov velocity process is introduced to simulate ensemble transport in highly heterogeneous continuum scale conductivity fields. This is the first stochastic model to simulate dispersion in high-variance conductivity fields for both Gaussian and exponential correlation structures.
Book Synopsis Fluid Flow and Transport in Porous Media, Mathematical and Numerical Treatment by : Zhangxin Chen
Download or read book Fluid Flow and Transport in Porous Media, Mathematical and Numerical Treatment written by Zhangxin Chen and published by American Mathematical Soc.. This book was released on 2002 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The June 2001 conference brought together mathematicians, computational scientists, and engineers working on the mathematical and numerical treatment of fluid flow and transport in porous media. This collection of 43 papers from that conference reports on recent advances in network flow modeling, parallel computation, optimization, upscaling, uncertainty reduction, media characterization, and chemically reactive phenomena. Topics include modeling horizontal wells using hybrid grids in reservoir simulation, a high order Lagrangian scheme for flow through unsaturated porous media, and a streamline front tracking method for two- and three- phase flow. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
Book Synopsis Mathematical and Numerical Modeling in Porous Media by : Martin A. Diaz Viera
Download or read book Mathematical and Numerical Modeling in Porous Media written by Martin A. Diaz Viera and published by CRC Press. This book was released on 2012-07-24 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete
Book Synopsis Non-fickian Solute Transport in Porous Media by : Don Kulasiri
Download or read book Non-fickian Solute Transport in Porous Media written by Don Kulasiri and published by Springer. This book was released on 2015-05-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.
